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Continuum-wise expansiveness for discrete dynamical systems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In the paper, we will prove that if a continuum-wise expansive homeomorphism f of a compact connected metric space X has a local product structure then it has a periodic point. Moreover, if a nontrivial transitive set of a diffeomorphism f of a compact smooth Riemannian manifold M is \(C^1\) stably continuum-wise expansive then it is hyperbolic. These results generalize those of Mañé (Topology 17:383–396, 1978) and Lee and Park (Dyn Syst 33:228–238, 2018).

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Acknowledgements

The author would like thank to the referee for careful reading of the manuscript and valuable comments.

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  1. Department of Marketing Big Data and Mathematics, Mokwon University, Daejeon, 302-729, South Korea

    Manseob Lee

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  1. Manseob Lee
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Correspondence to Manseob Lee.

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Lee, M. Continuum-wise expansiveness for discrete dynamical systems. RACSAM 115, 113 (2021). https://doi.org/10.1007/s13398-021-01056-w

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